Ferromagnetism in Hubbard Models
Hal Tasaki
TL;DR
This paper provides the first rigorous examples of Hubbard models in arbitrary dimensions that exhibit ferromagnetism at zero temperature, confirming long-standing theoretical predictions.
Contribution
It introduces the first non-singular Hubbard models with finite-range hoppings and Coulomb interactions that demonstrate ferromagnetism rigorously at zero temperature.
Findings
Hubbard models can exhibit ferromagnetism at zero temperature.
Finite-range hoppings and Coulomb interactions are sufficient for ferromagnetism.
The results confirm the long-standing Heisenberg-based picture of Coulomb-induced ferromagnetism.
Abstract
We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-ranged hoppings, dispersive bands, and finite on-site Coulomb interaction U. The picture, which goes back to Heisenberg, that sufficiently large Coulomb interaction can revert Pauli paramagnetism into ferromagnetism has finally been confirmed in concrete examples.
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